#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
using ll = long long;
ll n, m, s, t, l, k, p, ans;
vector <vector <pair <int, ll>>> g(3e5);
vector <ll> d1(3e5, 1e18);
vector <ll> d2(3e5, 1e18);
vector <ll> e;
vector <ll> f;
void dijkstra(int x, vector <ll>& d) {
priority_queue <pair <ll, int>> q;
vector <bool> done(3e5, false);
d[x] = 0;
q.push({ 0,x });
while (q.size()) {
int a = q.top().second;
q.pop();
if (done[a]) continue;
done[a] = true;
for (auto p : g[a]) {
ll b = p.first, c = p.second;
if (d[a] + c < d[b]) {
d[b] = d[a] + c;
q.push({ -d[b],b });
}
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> m >> s >> t >> l >> k;
ll a, b, c;
for (int i = 0; i < m; i++) {
cin >> a >> b >> c;
g[a].push_back({ b,c });
g[b].push_back({ a,c });
}
dijkstra(s, d1);
dijkstra(t, d2);
if (d1[t] <= k) { cout << n * (n - 1) / 2; return 0; }
e.resize(n);
f.resize(n);
for (int i = 0; i < n; i++) {
e[i] = d1[i + 1];
f[i] = d2[i + 1];
}
sort(e.begin(), e.end());
sort(f.begin(), f.end());
p = n - 1;
for (int i = 0; i < n; i++) {
while (p >= 0 && e[i] + f[p] + l > k) p--;
ans += p + 1;
}
cout << ans;
}
